The South African campus protests of 2015-17 in demand of decolonisation and free tertiary education presaged similar demonstrations on campuses throughout the English-speaking world and revealed the dilemmas of university leadership under conditions of sustained crisis. This research examines the typology of leadership exercised by senior administrators in South African higher education in the period just prior to these events, when the tensions that led to them were already manifest. It proposes a new conceptual model for leadership in higher education that will allow leaders to move beyond the bureaucracy and enable a conception of leadership as a complex interactive dynamic through which adaptive outcomes can emerge. Complexity theory frames the study, as it reconceptualises leadership by focusing on the dynamic interactions between all individuals within organisations; explains how those interactions can, under certain conditions, produce positive outcomes; and takes into account the properties of non-linearity, uncertainty, ambiguity and disequilibrium under which universities worldwide operate. A Likert-scale survey of senior higher-education leaders produced data that were analysed using both linear and non-linear statistical methods. The study finds that no distinctive leadership characteristics are evident at the senior levels of South African higher education management and that there are no significant differences between the leadership characteristics of senior managers in the country's historically white, historically black, and post-apartheid universities. An appreciation for complexity is critical within a university environment where bureaucratic assumptions are often the mode of operation. This article proposes a new model for leadership in higher education that will allow leaders to move beyond the bureaucracy and enable a conception of leadership as a complex interactive dynamic through which adaptive outcomes can emerge.